Was chatting with a shop owner who prefers premium gas even in cars that don't require it. This is not only because of knock resistance and fuel economy, but also because it has a lower level of impurities. Taking that for granted, and given the value of cleanliness in an engine, this makes some sense in the abstract. Though, whether this would make premium worth the money is another matter.
This all got me thinking. I can't assess the point about cleanliness, but I can do some back-of-the-envelope math to see if there's any chance a longevity benefit could pan out, regardless of how regular and premium differ.
If the only reason you clicked was to get mad at what you thought the answer would be, I'll save you the trouble: For engines that don't require premium, the most likely answer is no. At least, not according to what I found.
Caveats before you read further:
1. Nothing below says anything definitive whatsoever. This model is not another "index" or any of that junk. It's a crude thought experiment with some simple math. In some cases it might – might – yield inferences good enough for making practical decisions, which is all I wanted from it. In other cases it might yield some entertainingly weird results. Please, please don't pretend there's anything more to it than that.
2. This does not apply to engines that require premium gas.
The way I approached it was basically to compare per-mile costs of fuel and engine rebuilds for regular and premium gas. The math had several steps, but it's all basic:
1. [price per gallon of fuel] ÷ [mpg with that fuel] = [per-mile cost of that fuel]
For regular gas, I just filled in current numbers. For premium, I used the current price and generously assumed an mpg increase.
2. [cost of engine rebuild] ÷ [engine rebuild interval] = [per-mile cost of engine rebuild]
For regular gas, I made assumptions based on people's typical experiences. For premium, I kept the same number for engine rebuild cost but left the rebuild interval as an unknown.
3. [per-mile cost of regular] + [per-mile cost of engine rebuild w/ regular] = [per-mile cost of premium] + [per-mile cost of engine rebuild w/ premium]
4. Because each of the terms above is a fraction, the equation can be rearranged to isolate the unknown – i.e., the engine rebuild interval with premium:
Plugging in numbers on the left side of that equation and solving it should yield the minimum rebuild interval necessary to break even with premium gas. The engine would have to last at least that long for premium gas to be worth the money over regular.
I made a spreadsheet with all of this and threw in some numbers to play around. Here are some example outcomes:
Here, the model suggests the engine would have to last >2x as long on premium than on regular for the fuel price to be worth it. Not a chance in heck of that happening.
More:
Even more ludicrous numbers. I'm sure most of us are on the same page about this but the numbers really drive the point home IMO.
See that negative sign here? That means the model suggests premium gas wouldn't be worth using in that scenario even if it made the engine last literally forever. In other words, given these numbers, it'd be cheaper to run regular and rebuild the engine when it dies than to run premium and have the engine be immortal.
I also tried plugging in numbers like what I've seen at sketchy no-name stations vs. Top Tier stations around here:
Awkward.
Not actually worried by that last one. The model doesn't properly account for the elevated risk of a truly bad batch of gas from a sketchy station, which IMO is enough of a reason to write off sketchy gas and render the comparison moot.
Something else this doesn't account for: the fact that, the longer the engine runs, the higher the probability that it'll encounter a bad batch of gas or some other catastrophic event that'll cut its life short. That makes those long rebuild interval estimates even more hideously unlikely.
So, again, nothing definitive, but... seems safe to say any supposed benefits of premium gas in a car that doesn't require it are sketchy at best.
What do y'all think?
This all got me thinking. I can't assess the point about cleanliness, but I can do some back-of-the-envelope math to see if there's any chance a longevity benefit could pan out, regardless of how regular and premium differ.
If the only reason you clicked was to get mad at what you thought the answer would be, I'll save you the trouble: For engines that don't require premium, the most likely answer is no. At least, not according to what I found.
Caveats before you read further:
1. Nothing below says anything definitive whatsoever. This model is not another "index" or any of that junk. It's a crude thought experiment with some simple math. In some cases it might – might – yield inferences good enough for making practical decisions, which is all I wanted from it. In other cases it might yield some entertainingly weird results. Please, please don't pretend there's anything more to it than that.
2. This does not apply to engines that require premium gas.
The way I approached it was basically to compare per-mile costs of fuel and engine rebuilds for regular and premium gas. The math had several steps, but it's all basic:
1. [price per gallon of fuel] ÷ [mpg with that fuel] = [per-mile cost of that fuel]
For regular gas, I just filled in current numbers. For premium, I used the current price and generously assumed an mpg increase.
2. [cost of engine rebuild] ÷ [engine rebuild interval] = [per-mile cost of engine rebuild]
For regular gas, I made assumptions based on people's typical experiences. For premium, I kept the same number for engine rebuild cost but left the rebuild interval as an unknown.
3. [per-mile cost of regular] + [per-mile cost of engine rebuild w/ regular] = [per-mile cost of premium] + [per-mile cost of engine rebuild w/ premium]
4. Because each of the terms above is a fraction, the equation can be rearranged to isolate the unknown – i.e., the engine rebuild interval with premium:
Plugging in numbers on the left side of that equation and solving it should yield the minimum rebuild interval necessary to break even with premium gas. The engine would have to last at least that long for premium gas to be worth the money over regular.
I made a spreadsheet with all of this and threw in some numbers to play around. Here are some example outcomes:
Here, the model suggests the engine would have to last >2x as long on premium than on regular for the fuel price to be worth it. Not a chance in heck of that happening.
More:
Even more ludicrous numbers. I'm sure most of us are on the same page about this but the numbers really drive the point home IMO.
See that negative sign here? That means the model suggests premium gas wouldn't be worth using in that scenario even if it made the engine last literally forever. In other words, given these numbers, it'd be cheaper to run regular and rebuild the engine when it dies than to run premium and have the engine be immortal.
I also tried plugging in numbers like what I've seen at sketchy no-name stations vs. Top Tier stations around here:
Awkward.
Not actually worried by that last one. The model doesn't properly account for the elevated risk of a truly bad batch of gas from a sketchy station, which IMO is enough of a reason to write off sketchy gas and render the comparison moot.
Something else this doesn't account for: the fact that, the longer the engine runs, the higher the probability that it'll encounter a bad batch of gas or some other catastrophic event that'll cut its life short. That makes those long rebuild interval estimates even more hideously unlikely.
So, again, nothing definitive, but... seems safe to say any supposed benefits of premium gas in a car that doesn't require it are sketchy at best.
What do y'all think?
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